The two creative topics for this year were a graph of graph classes, and a tic-tac-toe state graph. The goal was to visualize each graph with complete artistic freedom, and with the aim of communicating the data in the graph as well as possible.
We received 6 submissions for the first topic, and 7 for the second. For each topic, we selected three contenders for the prize, which were printed on large poster boards and presented at the Graph Drawing Symposium. Finally, out of those three, we selected the winning submission. We will now review the top three submissions for each topic (for a complete list of submissions, refer to http://www.graphdrawing.de/contest2015/results.html).
2.1 Graph Classes
The Information System on Graph Classes and their Inclusions (ISGCI)Footnote 1 is an initiative to provide a large database of graph classes and their relations, as well as the complexity of several problems that are hard on general graphs. So far, data of 1,511 graph classes and 179,111 inclusions has been collected.
For the first creative topic, participants needed to draw the graph of the graph classes provided by the ISGCI database that are planar. Each node represents a graph class, and each (directed) edge represents an inclusion. For example, the edge from “outerplanar” to “cactus” says that every cactus is outerplanar.
The graph has 65 vertices and 101 edges. The graph is presented in the GraphML File FormatFootnote 2.
The resulting layout of the graph should contain the label of the vertices, provided as the description of the nodes, and should give a good overview on the hierarchy of the graph classes.
Runner-Up: Evmorfia Argyriou, Michael Baur, Anne Eberle, and Martin Siebenhaller (yWorks). The committee liked the use of edge grouping for nodes with many outgoing edges (such as the “planar” node and the use
of visual bridges to reduce the visual ambiguity at crossings. Also, the drawing makes good use of the available space and uses color as an additional cue to encode distance from the root.
Runner-Up: Megah Fadhillah (University of Sydney). The committee really liked the idea of having a large ”planar” node at the top, which acts as a title for the drawing and immediately explains what is being shown. The drawing uses color to show clusters of nodes and size to encode distance from the root.
Winner: Tamara Mchedlidze (Karlsruhe Institute of Technology). The committee likes the visual appeal of the drawing. The use of circular arcs for edges makes it easy to follow each individual edge, even when they pass behind
vertices (something which is traditionally considered bad practice in graph drawing). The drawing uses color to single out three meaningful groups of nodes: tree classes, bounded degree classes, and grid-like classes. The author also put a lot of thought into abbreviating node labels to increase the readability of the final drawing.
Tic-Tac-ToeFootnote 3 is a tactical two-player game in which two players take turns entering symbols (X or O) into cells of a three-by-three grid, with the objective of creating a row, column, or diagonal of equal symbols. The game is famous for its relative simplicity.
For the second creative topic, participants were asked to draw the graph of all possible Tic-Tac-Toe game states, in a way that shows as much of the structure and hidden information in the graph as possible. Each node represents a class of symmetric board positions, and there is an edge between two nodes u and v if a board position from v can be reached from a board position from u.
Runner-Up: Remus Zelina, Sebastian Bota, Siebren Houtman, and Radu Balaban (Meurs). The committee really liked visual appeal of the full drawing, which clusters the individual node into groups based on the ply (number of moves played) and the current winner after optimal play. This way, the drawing clearly shows a much smaller meta-graph (25 nodes and 39 edges) with
colors encoding the game state and “size” of clusters encoding the number of actual board positions that belong to that state. This drawing nicely communicates the global structure of the game.
Runner-Up: Evmorfia Argyriou, Michael Baur, Anne Eberle, and Martin Siebenhaller (yWorks). The second runner-up submitted an interactive visualization of the graphFootnote 4. The committee liked the idea of using an interactive tool to explore the state graph. Using the tool, you can really see the impact of each move, making it very useful for understanding the game. The tool will dynamically show the local neighborhood (all possible paths to get to the situation, and all possible continuations) for any board position. Using small colored disks, the winner after optimal play is visualized for individual nodes.
Winner: Jennifer Hood and Pat Morin (Carleton University). The committee was impressed by the way this drawing manages to illustrate the global structure of the graph while still making it possible to follow individual paths and board positions. The global structure is nicely visualized by presenting the nodes in three columns, indicating which player will win upon optimal play, and nine rows, indicating the ply of the positions. Edge colors distinguish between move types (optimal or non-optimal, which player made the move, and which player wins). The committee especially liked the use of variable node sizes, making them small where necessary without affecting other parts of the
drawing. Similarly, the committee liked the use of solid edges for the (relatively) small set of optimal-play edges and more faded colors for the non-optimal-play edges. Presenting the optimal-play edges (straight) in a different style than the non-optimal-play edges (orthogonal) further enhances their visual distinction.